Families of rationally connected varieties
Tom Graber, Joe Harris, Jason Starr
TL;DR
This paper proves that any one-parameter family of rationally connected varieties over an algebraically closed field of characteristic zero always admits a section, confirming a significant property of these varieties.
Contribution
It establishes the existence of sections for families of rationally connected varieties, advancing understanding of their geometric structure.
Findings
Existence of sections for one-parameter families of rationally connected varieties.
Supports conjectures about rational points in algebraic geometry.
Enhances knowledge of the structure of rationally connected varieties.
Abstract
We prove that a one-parameter family of rationally connected varieties (over an algebraically closed field of characteristic 0) always has a section.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation